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Peng-Robinson predictions for hydrocarbons, CO2, N2, and H2 S with pure water and NaCI brine
Fluid Phase Equilibria, 77 (1992) 217-240
217
Elsevier Science Publishers B.V., Amsterdam
Peng-Robinson predictions for hydrocarbons, CO,, N,, and H,S with pure water and NaCl brine Ingolf Sgreide a and Curtis H. Whitson Dept. of Petroleum. Eng., UNIT-NTH, 7036 Trondheim (Norway)
(Received March 4, 1991; accepted in final form February 2, 1992)
ABSTRACT Soreide, I. and Whitson, C.H., 1992. Peng-Robinson predictions for hydrocarbons, and H,S with pure water and NaCl brine. Fluid Phase Equilibria, 77: 217-240.
CO,, N,
Attempts at predicting mutual solubilities with a conventional cubic equation of state (EOS) including the effect of salts in the aqueous phase have so far been limited. The main purpose of this work is to provide a simple and novel approach for predicting mutual solubilities of brine/hydrocarbon mixtures with an EOS at high pressures and temperatures, including the effect of salinity in the aqueous phase. The Peng-Robinson EOS * has been applied in this study with two modifications: (1) an o-term in the EOS constant a has been developed specifically for the water/brine component as a function of sodium chloride (NaCl) brine salinity and pure water reduced temperature, T,, and (2) two sets of binary interaction parameters (BIP) in the classical mixing rule for mixture EOS constant a have been determined as a function of acentric factor, temperature, and salinity. Experimental data of vapor pressures and mutual solubilities provide the basis for the proposed methods. Applications of the methods described include phase behavior prediction of reservoir gas-oil/brine systems at high pressures, including (11 gas solubility in water/brine and (2) water solubility in hydrocarbon reservoir fluids.
INTRODUCTION
Most naturally occurring petroleum reservoir fluids contain water or brine. Conventional equations of state (EOSs), e.g. the PR EOS or the Correspondence
to: I. Soreide, Norsk Hydro a/s, P.O. Box 200, Stabekk, N-1321, Norway. a Current address: see Correspondence address. * Robinson and Peng, 1978.
0378-3812/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved
218
I. S@reide and C.H. Waitson /Fluid Phase Equilibria 77 (1992) 217-240
Soave-Redlich-Kwong EOS (Soave, 19721, are not adequate for representing the special interaction of water molecules that determines phase behavior of the aqueous phase in hydrocarbon-water binary mixtures. Typically, the aqueous phase gas solubility may be predicted orders of magnitude in error, while predicted compositions of the hydrocarbon-rich phase(s) are reasonably accurate. Several modifications to cubic EOSs have been proposed to achieve a better representation of mixtures including pure water. Peng and Robinson (1980) propose two modifications of the original PR EOS to improve phase behavior prediction of hydrocarbon mixtures including water: first, a specific temperature dependency of the EOS constant a for water, c.u(T,>,is expressed &* = 1.008568 + 0.8215 (1 - ,“*),
T, < 0.72
(1)
Equation (1) results in improved water vapor pressure predictions in the range 0.44 < T, < 0.72 compared with the original PR EOS a-term. Secondly, two sets of binary interaction parameters (BIPs) are proposed for hydrocarbon/water binaries, one set for the non-aqueous phase(s) and one set for the aqueous phase. There is a clear empirical advantage of using this procedure, but it may lead to a thermodynamic inconsistency using two different values of constant a (Robinson et al., 1985). Despite this inconsistency, the approach should be valid away from critical conditions, which are usually not obtained for hydrocarbon/water mixtures. Peng and Robinson (1980) applied the modified PR EOS to several binary mixtures including water and hydrocarbons (C,-nC,) and nonhydrocarbons commonly found in petroleum mixtures (N,, CO,, H,S). A constant BIP for the non-aqueous phase(s) and a temperature-dependent BIP for the aqueous phase were found adequate to match experimental mutual solubility data with reasonable accuracy. A review of various EOS mixing rules for aqueous solutions is given by Michel et al. (1989). Effect
of salts in the aqueous phase
Attempts at predicting mutual solubilities with an EOS including the effect of salts in the aqueous phase have so far been limited. Most of the studies concerning this problem are performed at low pressures and temperatures, or use methods that are not readily applicable to systems containing supercritical gases. The work by Harvey and Prausnitz (1989) proposes an EOS for high pressure conditions using a rather complex EOS which accounts for intermolecular forces due to ionic effects, in addition to describing conventional intermolecular forces for non-electrolytes. In this model, two BIPS included in a cubic mixing rule are obtained from
I. Speide and C.H. Whitson /Fluid
Phase Equilibria 77 (1992) 217-240
219
room-temperature osmotic coefficients and Seconov (Setchenow) constants. Results show that the prediction is good for systems including pure water or brine with low salt content (< 1 molal). The salting-out effect is, however, underpredicted for systems with moderate to high salt content. The main purpose of this work is to provide a simple and novel approach for predicting mutual solubilities of brine/ hydrocarbon mixtures with a cubic EOS at high pressures and temperatures, including the effect of salinity in the aqueous phase. The PR EOS has been applied in this study with two modifications: (1) an a-term in the EOS constant a has been developed specifically for the water/ brine component as a function of NaCl brine salinity and pure water reduced temperature, and (2) two sets of BIPs in the classical mixing rule for mixture EOS constant a have been determined as a function of acentric factor, temperature and salinity. Experimental data on vapor pressures and mutual solubilities provide the basis for the proposed methods. Applications of the modified EOS include phase behavior prediction of reservoir gas-oil/ brine systems at high pressures, including (1) gas solubility in water/ brine and (2) water solubility in hydrocarbon reservoir fluids. HYDROCARBONSOLUBILITYIN WATER/NaCl BRINE SOLUTIONS Interstitial or connate formation water in a petroleum reservoir contains varying amounts of different salts, though mainly NaCl. The presence of salts in formation water reduces the gas solubility. A major part of this work is aimed at predicting the effect of brine salinity on gas solubilities in aqueous brine mixtures. Since data on some gas solubility of hydrocarbons in brine do not exist, “experimental” data were generated using measured gas solubilities in distilled water and Seconow salting-out coefficients to adjust for the salinity effect on solubility. This procedure is described below: A correction for gas solubility in a brine, S,, compared with gas solubility in distilled water, S,, is given by Seconow in terms of a salting-out coefficient, k,, and salinity (molal), c,: S”/S, = 10-k~C~~ (2) where S has units of moles/litre (molarity); k, coefficients have been presented in the literature for various hydrocarbon/ brine systems, as reviewed by Long and McDevit (1952) and Zemaitis et al. (1986). Cramer (1984) reports k, coefficients for a one molal methane/NaCl brine binary mixture in the temperature range 0-300°C (32-572°F). These data may be fitted using the following relation: k, = 0.1813 - 7.692 x 10-4T + 2.6614 x 10+T2 - 2.612 x 10-9T3 (3)
I. S@reideand C.H. Whitson/Fluid Phase Equilibria 77 (1992) 217-240
220
where T is in “F. Pawlikowski and Prausnitz (1983) suggest a linear relation for k, in terms of (Ei/k): k, =A, + B,( q/k)
(4)
where ci is the Lennard-Jones energy interaction parameter for the gas component and k is Boltmann’s constant, and A, and 8, are temperature-dependent constants given specifically for each salt at 25°C (77°F). If we assume an analogous k, temperature dependency for hydrocarbons other than methane, eqn. (4) can be used to obtain the shift in the salting-out coefficient for ethane, propane and n-butane, ksi, relative to that for methane, k,,. ksi = k,, + Aksi
i =
(5)
C,,C3, nC,
where Ak,i is expressed as
Aksi= ‘s[ (Ei/k) - (El/k)]
(6)
Pawlikowski and Prausnitz report B, = 3.56 x 1O-4 K m-l for NaCl brine. e/k may be related to the normal boiling point of the gas, Tbi.
(7)
Ei/k = 1.25T,, with Tbi in K. A general (3)-(7X
ksi correlation
results from combining
eqns.
k,, = 0.13163 + 4.45 x 10-4T,i
- 7.692 x 10-4T + 2.6614 x 10+T2 - 2.612 x 10-9T3
(8)
with T in “F and Tbl in K. Figure 1 shows a plot of salting-out coefficients versus temperature. The continuous lines represent k, values estimated from eqn. (8) and the symbols represent k, values for NaCl brines reported by Cramer (1984), Morrison (1952), Morrison and Billett (19521, Long and Chierici (1961) and Standing (1974). The accuracy of k, at high temperatures for C,, C, and nC, is questionable, but the importance of an accurate relation for these components at high temperatures is also small. Now that a general salting-out coefficient relation (eqn. (8)) has been developed, the hydrocarbon solubility in NaCl brine may be calculated to provide an “experimental” database of hydrocarbon solubility as a function of temperature and salinity as follows: (1) Obtain experimental data for hydrocarbon mole fraction in pure water, xi, at specified pressure and temperature conditions. (2) Calculate gas-water solubility, S, (S, = Nx,/(l -xi), where N is a constant dependent on units and brine properties).
I. Sereide and C.H. Whitson /Fluid
Phase Equilibria 77 (1992) 217-240
221
,, ,, o METHANE q 9 o ETHANE d A d PROPANE o o o n-BUTANE
ff”% 0 O,‘Oo5
10I,,,,
a 0
I,,@,,,,,,,,,,,,,,,,
REDU&
TE%t?AT&
30
35
T,
Fig. 1. Salting-out coefficients vs. hydrocarbon reduced temperature for hydrocarbon/NaCl brine mixtures: symbols represent reported coefficients from various sources, and solid lines represent eqn. (8).
(3) Calculate the ratio SJS,
from eqn. (21, with ksi estimated from eqn. solubility, S,, is then determined from the SJS, ratio
(8). Gas-brine and S,. (4) Finally, calculate S,/W + SJ.
the hydrocarbon
mole fraction in brine, xin (xi,, =
EOS MODIFICATIONS
Vapor pressure
Experimental vapor pressure data for water are given by Schmidt (1979) from 0 to 325°C [32 to 617”F], and for NaCl brine solutions of 0 to 5.0 molality from 80 to 325°C (176 to 617°F) by Haas (1976). The constant a of the PR EOS was modified for water/ brine to fit these data, resulting in a relation for the a-term as a function of pure water reduced temperature, T,, and salinity, c,,: (Y1’2= 1 + 0.4530[1 - T,(l - o.o103c:;‘)] + O.O034(T;_3- 1)
(9)
For water the PR EOS modified with eqn. (9) predicts vapor pressure within 0.2% error from 15 to 325°C [60 to 617”F]. NaCl brine vapor
I. Sereide and C. H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
222
pressures (176°F).
may be estimated
with about the same accuracy above 80°C
Aqueous and non-aqueous phase BIPs
The EOS modification proposed by Peng and Robinson (1980) using two sets of BIPs for water-hydrocarbon solutions has been adopted in this work. For a mixture including components i and j, two different EOS constants a are determined for the non-aqueous and the aqueous phase: a:* and aeQ, respectively. These are expressed as a function of the respective phase BIPs, kiyA and kz$Q, and mole fractions y and X. a!* = c lJ afiQ = i i
xyiyj(aia,)1’2(1
- k$*)
ixixj(aiaj)1’2(l
- kGQ)
w4
WV
j
Non-aqueous-in-aqueous phase solubilities
The sources for experimental hydrocarbon solubility data in pure water (C,-nC,/H,O) used in this work are listed in Table 1. Figure 2 shows that excellent agreement with measured methane solubilities in water can be obtained with the proposed EOS modifications (eqns. (9) and (10)) at various pressures and temperatures. The kzcQ values of eqn. (10) were determined by regression. The following correlation was developed: keQ=A fJ
0
+A 1T.+A rl
2 T? rl
(11)
where i = hydrocarbon components and j = water, and the constants A,, A, and A, are given in Table 2. The correlation may also be extrapolated to estimate kLcQ for pentane and heavier components. Figure 3 compares kcQ from eqn. (11) (solid line) with the regression-based kQQ (symbols).
TABLE 1 References
reporting hydrocarbon
gas solubilities in pure water
System
Reported by
p (bar)
T (“C)
Cl /I-W
CuIberson and McKetta (1951) Culberson and McKetta (1950) Kobayashi and Katz (1953) Reamer et al. (1952)
14-690 14-690 14-207 14-690
25-171 100-171 100-154 100-171
CZ /HP C3 /H,O n-C‘, /H,O
I. S@eide and C.H. Whitson /Fluid SYSTEM: 700 c
00001
Phase Equilibria 77 (1992) 217-240
223
C,/HpO 1
MOLE
‘
z
FRACTION
1 0.001
METHANE
IN
L
AQUEOUS
PHASE.
xc,
0.01
Fig. 2. Measured (symbols) and PR EOS calculated (solid lines) methane solubility in the aqueous phase at various pressures and temperatures.
Table 3 lists the physical properties used during development of eqns. (9) and (11). Figure 4 compares generated methane solubilities (using the above procedure) in a NaCl brine of various salinities at 104°C (220°F) (symbols) with methane solubilities calculated from the modified PR EOS using best-fit keQ values (solid lines). A ktQ correlation for hydrocarbon/NaCl brine binaries was developed from these data, and is expressed in terms of hydrocarbon Tri and c,: k;Q =A,(1
+ (Y,,c,,) +A&,(1
+ arc,,)
+A,T;(l
+ (Y~c,)
(12)
The constants of eqn. (12) are listed in Table 2. Equation (12) was developed for methane, ethane, propane and n-butane in 0 to 5 molal
TABLE 2 Constants in eqns. (11) and (12) A0 AI A2 a0
a1 a2
-
1.1120-1.73690-“~’ 1.1001+0.8360w~ 0.15742- l.O988o, 4.7863 x lo- 1304 1.4380 x lo-’ ’ 2.1547 x 1O-3
I. Sereide and C. H. whitson /Fluid Phase Equilibria 77 (1992) 217-240
224
0.1 ~""""',""""',""""',""""',
-0.3 r'JJ""J 05
l""""'l""'l""'l,"lt,'l' aEOD"CED
25
&ER*nJREf~,
Fig. 3. Aqueous phase interaction parameters for hydrocarbon/water binary systems as a function of hydrocarbon reduced temperature: symbols represent values determined by fitting experimental solubility data and solid lines are calculated using eqn. (11).
NaCl brine, for the pressure ranges given in Table 1, and at temperatures between 38 and 204°C (100 and 400°F). Figure 5 shows kc” versus temperature for methane dissolved in NaCl brine of varying salinity.
TABLE 3 Physical properties of components Component
Mol. weight
Carbon dioxide Hydrogen sulfide Nitrogen Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane Water
44.0 34.1 28.0 16.0 30.1 44.1 58.1 58.1 72.2 72.2 86.2 18.0
304.2 373.2 126.1 190.6 305.4 369.8 408.1 425.2 460.4 469.6 507.4 647.3
PC (bar)
Acentric factor
73.8 89.4 34.0 46.0 48.8 42.5 36.5 38.0 33.8 33.7 30.1 221.2
0.2273 0.1081 0.0403 0.0108 0.0998 0.1517 0.1770 0.1931 0.2275 0.2486 0.3047 0.3434
194.7 212.8 77.3 111.6 184.6 231.1 261.3 272.7 301.0 309.2 341.9 373.2
I. S@reide and C.H. W&on SYSTEM:
/Fluid
Phase Equilibria 77 (I 992) 217-240
225
C,/NaCI-BRINE
BRINE SALINITY, c,. 00000000 m q ooao 0.66 m IA&&a 171 m ob0PP 3.42 m +++++513 m
MOLE
FRACTION
METHANE
IN AQUEOUS
PHASE,
xc!
Fig. 4. Generated (symbols) and PR EOS calculated (solid lines) methane solubility in the aqueous phase at 104°C as a function of pressure and brine salinity.
The following kGQ correlations were developed for binaries including water/brine and N,, CO, and H,S, based on experimental data referred to in Table 4:
0.2
7
BRINE 00000 OliDDD obc.*d bbbbb +++++
0.1
SYSTEM:
C,/NaCI-BRINE
(8 18 ‘I”,,
I”“““““,”
SALINIM.
c,.
0.0 0.65 1.71 2 56 3 42
.T Y ;
0.0
: v, ;
-0.1
5 -0.2
-0.3
30
Fig. 5. Aqueous phase interaction parameters for methane/NaCl brine binary systems as a function of temperature and brine salinity: symbols represent best-fit results and solid lines represent eqn. (12).
I. Sereide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
226
TABLE 4 References reporting nitrogen, water and NaCl brine
carbon dioxide and hydrogen sulfide solubilities
in pure
System
Reported by
p (bar)
T (“Cl
N, /H,O
Wiebe et al. (1933) O’Sullivan and Smith (1970) Wiebe and Gaddy (1940,194l) Prutton and Savage (1945) Takenouchi and Kennedy (1964) Yasunishi and Yoshida (1979) Selleck et al. (1952) Gillespie et al. (1984) Lee and Mather (1977)
14-103s lOO- 600 25- 510 25- 620 14- 970 1.0 20- 345 20- 220 lo60
25-100 52-125 12- 42 38- 50 150-350 15- 35 38-171 71-204 90-150
N, /brine Cb, /Ha0 CO2
/H,O
CO2 /brine CO2 /brine H,S/H,G H,S/H,G H,S/H,G
N,/NaCl
brine:
kcQ = - 1.70235( 1 + 0.25587~;!~) + 0.44338( 1 + O.O8126~,q;7~)T,, CO,/NaCl
brine:
kc0 = - 0.31092(1+
0.15587~~~~~~)+ 0.23580( 1 + 0.17837~,q;9~~)T,,
- 21.2566 exp( - 6.7222T,, - csW) H,S/NaCl
(13)
(14)
brine:
kcQ = - 0.20441+ 0.23426T,,
(15)
where i = N,, CO, or H,S, and j = water or brine. Figures 6 and 7 show keQ as a function of temperature and brine salinity for N,/ and CO,/NaCl brine binary mixtures, respectively. Symbols represent best-fit BIPs determined for the modified PR EOS, and solid lines represent BIPs calculated from correlation eqns. (13) and (14), respectively. The values increase linearly with increasing temperature for N,/NaCl brine mixtures. For COJNaCl brine mixtures it was observed that kcQ is a linear function of temperature above 150°C (300°F) and slightly non-linear below 150°C. Experimental data reporting solubility of CO, in NaCl brine for T < 150°C and at high pressures are not readily available. Therefore the dashed lines in Fig. 7 are not based on measured data, but rather a careful extrapolation of kij AQ determined at higher temperature. It is observed that the extrapolation of CO,/NaCl brine k,$” corresponds well to values obtained from solubility data reported by Yasunishi and Yoshida (1979) at atmospheric pressure (14.7 psia) in the range 15-35°C (60-95°F). A linear relation between kcQ and T,(H,S) was developed for the hydrogen sulfide/water binary mixture. This is illustrated in Fig. 8, which compares best-fit klqQ values obtained with the modified PR EOS and
I. Sereide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240 SYSTEM. 0.0
-
-02
-
i Q -0.3
-
J
N,/NaCI--BRINE
1
-01
227
I
2 In 3 -0.4
-
3 s Q -0.5
b
-0.6 t -o.7
r
0
I
1
25
1 I I
1
I
I
1
I
1
100 C
&PEW&E,
l
1 l
I
1
125
L I
1
Fig. 6. Aqueous phase interaction parameters for nitrogen/NaCl brine binary systems as a function of temperature and brine salinity: symbols represent best-fit results and solid lines represent eqn. (13).
SYSTEM:
CO/NaCI-BRINE
0.3
0.2
-0.2
~0000
Yasunishl and Yoshida 15 T p=, 0 bar
;::::
g: :g
c,=o-5
m
II,1,,IIIIII,,I,,I,,I,,I,IIIII,,,,,,,,,,,,,,
0
50
100 150 TEMPERATURE,
C
200
250
Fig. 7. Aqueous phase interaction parameters for carbon dioxide/NaCl brine binary systems as a function of temperature and brine salinity: symbols represent best-fit results and solid lines represent eqn. (14).
I. Stireide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
228
SYSTEM:
0.15
HzS/H,O
7
---___ gg----------___
0
:
PHASE
80
100 120 TEMPERATURE,
140
160
180
200
C
Fig. 8. Aqueous and non-aqueous phase(s) interaction parameters for hydrogen sulfide/water binary systems as a function of temperature: symbols represent best-fit results and solid lines represent eqns. (15) and (17) for k,qQ and k$*, respectively.
kcQ values from eqn. (15). Figure 9 compares experimental hydrogen sulfide gas solubilities with calculated values using the modified PR EOS and eqn. (15). The agreement is acceptable at low pressures. SYSTEM:
H&/Hz0
140v 20 _ _ _ 00 -
+
00000 30 oc 00000 71 oc 00000 104 oc +++++ 138 “C lxAfxl%b 171 oc
80 -
60 -
40 -
20 -
r,,,,,,~,,I~~~~~,~~~I~~~~~~~~~~~~~~~~~l~I
0900
MOLE
0.04
0.02
FRACTION
HIS
IN AQUEOUS
0.06
0.06
PHASE,
xw
Fig. 9. Measured (symbols) and PR EOS calculated (solid lines) hydrogen sulfide solubility in the aqueous phase at various pressures and temperature.
229
I. Sgreide and C.H. Whitson/Fluid Phase Equilibria 77 (I 992) 217-240 TABLE 5 Non-aqueous phase interaction light components
parameters,
ki,NA, for binary mixtures of water and various k?* I, 0.4850 0.4920 0.5525 0.5091 0.4778 0.1896 Eqn. 17
Component
Cl C, c3
n-C, N2 co2 H2S
Aqueous-in-non-aqueous phase solubilities
Experimental water solubility data in the non-aqueous phase for mixtures containing brine have not been available in the literature. Until such data become available it is recommended that the effect of salinity be modeled using the water/brine cy(c,)-term (eqn. (9)) in the PR EOS and a non-aqueous phase BIP value, k,y*, independent of salinity. k$* is basically independent of temperature, i.e. a constant kE* value results in water solubilities that are in good agreement with experimental data over the entire temperature range. kt” values are presented in Table 5. These are determined on the basis of pure water solubility data reported in references listed in Table 6. Figure 10 shows predicted water solubilities in the non-aqueous phase for a methane/NaCl brine mixture with varying brine salinity. The predicted reduction in water solubility for mixtures containing brine, relative
TABLE 6 References reporting non-hydrocarbon/water
non-aqueous systems
phase(s) water solubility for some hydrocarbon/
(bar)
System
Reported by
p
C,
/H,O
C,
/H,O
c3
/H20
Olds et al. (1942) Reamer et al. (1943) Kobayashi and Katz Reamer et al. (1952) Peng and Robinson (1985) Takenouchi and Kennedy (1964) Selleck et al. (1952) Gillespie et al. (1984) Lee and Mather (1977)
14-670 14-670 14-207 14-670 7-103 14-966 14-345 20-220 lo- 40
n-C, /H,O N, CO2
/H,O /H,O
H,S/H,G H,S/H,G H,S/H,G
T (“0 38-238 38-238 38-154 38-238 25-100 150-350 38-171 71-204 71
and
230
I. Sereide and C.H. whitson /Fluid Phase Equilibtia 77 (1992) 217-240 SYSTEM.
C,/NaCI-BRINE
600
T=lZl “C BRINE SALINITY, O? 0.0 q m 0 86 c+..%e 1.71 *u. 2.57 +u 3.42 *_cc!d 5.13
I
MOLE
0.01
FRACTION
2
WATER
5
IN C,-RICH
c,,
0.1
PHASE,
yv
2
Fig. 10. Measured (symbols) and PR EOS calculated (solid lines) water solubility in the non-aqueous phase of a methane/NaCl brine system at 121°C as a function of pressure and brine salinity.
to solubility for mixtures containing pure water, is for practical purposes independent of pressure and temperature. The ratio y,/yz calculated by the modified PR EOS is correlated against salinity in Fig. 11. The effect of
ODDOD OD(IDD a-
KATZ ET AL CALCULATED CALCULATED
BRINE
CORRECTION AT 38 ‘C AT 121 ‘C
SALINITY,
c,.
Fig. 11. Effect of brine salinity on water solubility in the non-aqueous vapor phase for a methane/NaCl brine mixture: “calculated” refers to use of the PR EOS modified with eqns. (9) and (10).
I. Sgreide and C. H. whitson /Fluid SYSTEM.
00000 00000 00000 +++++ *****
MOLE
38 71 93 138 171
FRACTION
Phase Equilibria 77 (1992) 217-240
231
H&/Hz0
o 0 “C “C “C
HpS
IN VAPOR
PHASE,
ytgi
Fig. 12. Measured (symbols) and PR EOS calculated hydrogen sulfide-rich vapor phase.
(solid lines) water solubility in the
salinity is clearly less than that reported by Dodson and Standing (1944) in the salinity range 0.0 to 0.6 molal, and is consistent with the correlation of Katz et al. (1959) up to a molality of about 3.0. The Katz y,/yz-relation can be expressed in terms of c, as y,(brine) yz(water)
p,(brine) 2: pz(water)
= 1 - 0 02865~‘.~ SW ’
(16)
where pw and y, represent vapor pressure and vapor phase mole fraction, respectively. For the H2S/H,0 system kt” is slightly dependent on temperature as shown in Fig. 8, resulting in the following relation: kF* ri = 0.19031-
0 .059653.l-l
i=H,S
(17)
Figure 12 shows that calculated water solubilities in the H,S-rich vapor phase compares well with experimental data, especially at pressures below 100 bar (1500 psi).
APPLICATIONS
In this section the proposed methods are applied to compare predicted mutual solubilities with measured data. Figure 13 compares predicted
I. S@reide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
232 SYSTEM: 700
,8
I
I
III,
I
I
C,/NaCI-BRINE, I,
I
I
,I
I
NaCI-BRINE c,=4.0
600
,I,
T=103 ”
’
“”
”
NaFl-j,ylJE ”
”
‘C ”
”
”
”
”
‘J
WATER
1
500 %
m
,-400
-
5 3300
-
E
a
$d;~LS
EXPERIMENTAL PR EOS PREDICTED
Fig. 13. Measured (symbols) and predicted (solid lines) methane solubility in the aqueous phase of a methane/NaCl brine system at 103°C as a function of pressure and brine salinity (experimental data from O’Sullivan and Smith, 1970).
methane solubilities in NaCl brine at 103°C with measured data reported by O’Sullivan and Smith (1970). Brine salinity ranges from 0.0 to 4.0 m, at pressures from 100 to 600 bar. It is observed that the PR EOS, modified with eqns. (9), (10) and (121, reproduces the experimental data accurately. Similar data are reported by Price et al. (1982) for C,/NaCl brine with salinity varying from 0.0 to 5.1 m, and pressures from 250 to 1550 bar. The comparison between predicted and measured data presented in Fig. 14 shows that C, solubility is slightly underestimated at 170°C at c, = 0.0, 1.9 and 5.1 m. The comparison shows that the deviations are most pronounced at high pressures (> 1000 bar). O’Sullivan and Smith also reported N, solubility in NaCl brine under similar conditions. A comparison of measured and predicted data is shown in Fig. 15. Again the modified PR EOS performs very well, except at C = 1.0 m where N, solubility is somewhat underpredicted. The aqueous phase liquid composition for a CO,/NaCl brine mixture is presented by Takenouchi and Kennedy (1965) at 150°C at pressures from 100 to 1400 bar. Figure 16 compares calculated and measured solubility data in the pressure range from 100 to 400 bar. Dodson and Standing (1944) reported measured solubilities of natural gas in pure water and in two oil-field brines. The pressure and temperature ranges in this study were 34.5-345 bar and 37.7-121°C. The salinity of the
I. Qreide and C. H. whitson /Fluid SYSTEM: 1750
C,/NaCI-BRINE,
Phase Equilibria 77 (1992) 217-240 T= 170
I,IIIIIII(IIIIIIIII,IIIJ~II~I,IIII,I NaCI-BRINE NO:‘-J;l;E c,=, 9 ”
233
‘C
WATER
1250 z m
1
- 1000 k! is 2
750
:
500
250
tL o?ooo I
MOLE
II
I
u c 10’)
0 005 FRACTION
1’8
METHANE
8
1’1 III )‘I 0 010 IN AQUEOUS
1’1 0015 PHASE,
1’8
l”j xc,
Fig. 14. Measured (symbols) and predicted (solid lines) methane solubility in the aqueous phase of a methane/NaCl brine system at 170°C as a function of pressure and brine salinity (experimental data from Price et al., 1982).
SYSTEM. 700
NoFl->:tE ” 600
N,/NaCI-BRINE,
T=103
“C
,IIIII,I~,II,,III,I(,,I,,,,,,,,,,,,,,,,,,,,,,,,,,NaCI-BRINE c,.=, 0
-
0
100
OPOOO MOLE
;YII;ILS
0.001 FRACTION
0 002 NITROGEN
WATER 0
EXPERIMENTAL PR EOS PREDICTED
0.003 ,,(,,,,,,,,,,, 0.004 IN AQUEOUS PHASE,
0.005 x,,,
Fig. 15. Measured (symbols) and predicted (solid lines) nitrogen solubility in the aqueous phase of a nitrogen/NaCl brine system at 103°C as a function of pressure and brine salinity (experimental data from &Sullivan and Smith, 1970).
I. Qreide and C. H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
234 SYSTEM.
CO,/NoCI-BRINE.
T= 150
OC
I~~~II~~“JI~~~I~‘JJIJJ~I”“~_
SYMBOLS,
tt
I
I
I
I
o”ooo MOLE
I
I
I
I
I
I
0.010 FRACTION
I
”
CO,
/
I
I
/
1 /
0 020 IN AQUEOUS
”
EXPERIMENTAL CALCULATED
11
1
0.030 PHASE,
”
1 ”
t
01
0.040 xco,
Fig. 16. Measured (symbols) and predicted (solid lines) carbon dioxide solubility in the aqueous phase of a carbon dioxide/NaCl brine system at 150°C as a function of pressure and brine salinity (experimental data from Takenouchi and Kennedy, 1964).
two brines denoted “Brine A” and “Brine B” were 8630 ppm (cSW= 0.15 m> and 34 1000 ppm (cSW= 0.60 m>, respectively. Although different types of salt were inchded in Brine A and Brine B, they were treated as NaC1
oPooo
,11111111111111111~IIIIII”‘~’
0 001 MOLE
FRACTION
0.003 0.002 NATURAL-GAS,
0 004 XNG
Fig. 17. Measured (symbols) and predicted (solid lines) natural gas solubility in the aqueous phase for the systems natural gas/water and natural gas/“Brine B” at 37.8”C (experimental data from Dodson and Standing, 1944).
I. Qreide and C.H. Whitson /Fluid
T=200 300
Phase Equilibria 77 (1992) 217-240
235
OF (93 3 “C)
-
MOLE
FRACTION
NATURAL-GAS,
X,,G
Fig. 18. Measured (symbols) and predicted (solid lines) natural gas solubility in the aqueous phase for the systems natural gas/water and natural gas/“Brine B” at 93.3”C (experimental data from Dodson and Standing, 1944).
brines. The natural gas used by Dodson and Standing contained 88.5 mol% C, and less than 1 mol% C,,; the average molecular weight of the gas was 19.
rY
2 -200
k! 2
Cl50
-
-
I? 100
-
50
0”000
I I I I I b I I, I I I I I I1 I I I1 I 0 003 0.002 0.001 MOLE FRACTION NATURAL-GAS, xw
I I I I 0 004
Fig. 19. Measured (symbols) and predicted (solid lines) natural gas solubility in the aqueous phase for the system natural gas/water at 121.1”C (experimental data from Dodson and Standing, 1944).
I. Sereide and C. H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
236 SYSTEM: c
NATURAL-GAS/WATER I
1 #‘II
4
$250 m
MOLE
FRACTION
WATER
IN VAPOR
PHASE,
yHa
Fig. 20. Measured (symbols) and PR EOS predicted (solid lines) water solubility in the hydrocarbon-rich vapor phase of a natural gas/water system at various temperatures (experimental data from Dodson and Standing, 1944).
To check performance of the proposed methods using the modified PR EOS for multicomponent mixtures, predicted natural gas solubilities were compared with the data of Dodson and Standing. These comparisons are presented in Figs. 17, 18, and 19 for 38, 94 and 121”C, respectively. It is shown that the predicted natural gas mole fraction in distilled water and in “Brine B” is very accurate, except for slight deviations at pressures above 250 bar at 121°C. Dodson and Standing also reported water solubility in the natural gas. Figure 20 shows that the prediction of these data is quite good when using the modified PR EOS and the kf;‘*‘s listed in Table 5. A k,y* value equal to 0.5 has been used for hydrocarbon/water binaries not listed in Table 5. For all hydrocarbon/ brine binaries eqn. (12) was applied to calculate ktQ.
CONCLUSIONS
Mutual solubilities have been accurately predicted with a modified,PR EOS for hydrocarbon/NaCl brine and some non-hydrocarbon/NaCl brine mixtures. The modifications consist of: (1) Using a modified a-term in the EOS constant a for the brine component as a function of water reduced temperature and brine salinity.
I. S@reide and C.H. Whitson /Fluid
Phase Equilibria 77 (1992) 217-240
231
(2) Using two sets of BIPs for each binary including water/ brine kbQ and kzyA for the aqueous phase and non-aqueous phase, respectively. k? is expressed as a function of NaCl brine salinity, hydrocarbon acentric factor and reduced temperature. Specific klyA correlations have also been developed for N,/, CO,/ and H,S/NaCl brine mixtures. For kt* a constant value is applied, except for klTA(H,S). The proposed methods have been demonstrated by comparing predicted and measured solubility of C,, N,, and CO, in NaCl brine of varying salinity. Acceptable accuracy has been obtained over a wide range of pressure and temperature conditions. Natural gas solubility in water and in two oil-field brines of varying salinity has been predicted with good agreement with measured data over a wide range of pressures and temperatures. Also, the predicted water solubility in natural gas agrees well with measured data.
ACKNOWLEDGMENT
This work was supported by the Nordic Council and Norwegian Foundation for Human and Technical Science.
LIST OF SYMBOLS
a, b a,,
al,
4 4, c SW C SW
k k% kk
ks MS P PC S” SW T Tb T,
4
a2,
a3
EOS constants constants of salting-out coefficient correlation constants of eqns. (11) and (12) constants of salting-out coefficient correlation brine salinity lo6 (m,/m, + m,) (ppm) brine salinity lo3 n,/m, (molality) Boltzmann’s constant aqueous phase interaction parameter for binary i, j non-aqueous phases interaction parameter for binary i, j salting-out coefficient, molality-‘, m-i molecular weight of salt (M, = 58.44 for NaCl) pressure (bar [psi]) critical pressure (bar [psi]) solution gas-brine ratio (mol-‘) (molarity) solution gas-water ratio (mall’) (molarity) temperature (“C [“F]) normal boiling point temperature (K [“RI) critical temperature (K [“RI)
238
I. Screide and C. H. whitson /Fluid Phase Equilibria 77 (1992) 217-240
T,
reduced temperature (T, = T/T,) normalized mole fraction of aqueous phase normalized mole fraction of non-aqueous phase
x, Yi
Greek letters a ai Aksi
E
w,
temperature-dependent parameter in EOS constant a constants of eqn. (12) shift in salting-out coefficient, m - ’ Lennard-Jones energy interaction parameter acentric factor
REFERENCES Cramer, SD., 1984. Solubility of methane in brines from 0 to 300°C. Ind. Eng. Chem. Process Des. Dev., 23: 300-305. Culberson, O.L. and McKetta, J.J. Jr., 1950. Phase Equilibria in Hydrocarbon-Water Systems. II The solubility of ethane in water at pressures to 10,000 psi, Trans. AIME, 189: l-6. Culberson, O.L. and McKetta, J.J., Jr., 1951. Phase equilibria in hydrocarbon-water systems. III The solubility of methane in water at pressures to 10,000 psi. Trans. AIME, 192: 319-322. Dodson, C.R. and Standing, M.B., 1944. Pressure-volume-temperature and solubility relations for natural gas-water mixtures. Drilling and Production Practice, API, 173-178. Gillespie, P.C., Owens, J.L. and Wilson, G.M., 1984. Sour water equilibria extended to high temperatures and with inerts present. Paper No. 34b presented at the AIChE Winter National Meeting, Atlanta, GA, March 11-14. Haas, J.L., Jr., 1976. Physical properties of the coexisting phases and thermochemical properties of the H,O component in boiling NaCl solutions. Geol. Surv. Bull., 1421-A and 1421-B. Harvey, A.H. and Prausnitz, J.M., 1989. Thermodynamics of high-pressure aqueous systems containing gases and salts. AIChE J., 35: 635-644. Katz, D.L., Cornell, D. and Vary, J.A., 1959. Handbook of Natural Gas Engineering. McGraw-Hill, New York. Kobayashi, R. and Katz, D.L., 1948. Methane-n-butane-water system in two- and three phase regions. Ind. Eng. Chem., 40: 5. Kobayashi, R. and Katz, D.L., 1953. Vapor-liquid equilibria for binary hydrocarbon-water systems. Ind. Eng. Chem., 45: 440-451. Lee, J.I. and Mather, A.E., 1977. Solubility of hydrogen sulfide in water. Ber. Bunsenges Phys. Chem., 81: 1021-1023. Long, F.A. and McDevit, W.F., 1952. Activity coefficients of nonelectrolyte solutes in aqueous salt solutions. Chem. Rev., 51: 119-169. Long, G. and Chierici, G., 1961. Salt content changes compressibility of reservoir brines. The Pet. Eng., B-25 to B-31. Ludecke, D. and Prausnitz, J.M., 1985. Phase equilibria for strongly nonideal mixtures form an equation of state with density-dependent mixing rules. Fluid Phase Equilibria, 22: 1-19.
I. S)reide and C.H. Whitson /Fluid
Phase Equilibria 77 (1992) 217-240
239
Markham, A.E. and Kobe, K.A., 1941. The solubility of carbon dioxide and nitrous oxide in aqueous salt solutions. J. Am. Chem. Sot., 63: 449-454. Michel, S., Hooper, H.H. and Prausnitz, J.M., 1989. Mutual solubilities of water and hydrocarbons from an equation of state. Need for an unconventional mixing rule. Fluid Phase Equilibria, 45: 173-189. Morrison, T.J., 1952. The salting-out of non-electrolytes. Part I. The effect of ionic size, ionic charge, and temperature. J. Chem. Sot., 3814-3818. Morrison, T.J. and Billett, F., 1952. The salting-out of non-electrolytes. Part II. The effect of variation in non-electrolyte. J. Chem. Sot., 3819-3822. Olds, R.H., Sage, B.H. and Lacey, W.N., 1942. Phase equilibria in hydrocarbon systems. Composition of the dew-point gas of the methane-water system. Ind. Eng. Chem., 34 (10): 1223-1227. O’Sullivan, T. and Smith, N.O., 1970. The solubility and partial molar volume of nitrogen and methane in water and in aqueous sodium chloride from 50 to 125°C and 100 to 600 atm. J. Phys. Chem., 74: 1460-1466. Pawlikowski, E.M. and Prausnitz, J.M., 1983. Estimation of Setchenow constants for nonpolar gases in common salts at moderate temperatures. Ind. Eng. Chem. Fundam., 22: 86-90. Peng, D.-Y. and Robinson, D.B., 1980. Two- and three-phase equilibrium calculations for coal gasification and related processes. In: S.A. Newman (Ed.), Thermodynamics of Aqueous Systems With Industrial Applications. ACS Symp. Ser., 393: 393-414. Price, L.C., Blount, C.W., MacGowan, D. and Wenger, L., 1982. In: D.G. Bebout, and A.L. Bachman (Eds.), Proc. Conf. on Geopressured-Geothermal Energy: US Gulf Coast, Louisiana State University, Baton Rouge, LA. Prutton, C.F. and Savage, R.L., 1945. The solubility of carbon dioxide in calcium chloridewater solutions at 75, 100, 120” and high pressure. J. Am. Chem. Sot., 67: 1550-1554. Reamer, H.H., Olds, R.H., Sage, B.H. and Lacey, W.N., 1943. Phase equilibria in hydrocarbon systems. Composition of the dew-point gas in the ethane-water system. Ind. Eng. Chem., 35: 790-793. Reamer, H.H, Sage, B.H. and Lacey, W.N., 1952. Phase equilibria in hydrocarbon systems. n-Butane-water system in the two-phase region. Ind. Eng. Chem., 44: 609-615. Robinson, D.B. and Peng, D.-Y., 1978. The Characterization of Heptanes and the Heavier Fractions, Research Report 28, GPA, Tulsa. Robinson, D.B., Peng, D.-Y. and Chung, S.Y.K., 1985. The Development of the PengRobinson equation and its application to phase equilibrium in systems containing methanol. Fluid Phase Equilibria, 24: 25-41. Schmidt, E., 1979. In: U. Grigull, (Ed.), Properties of Water and Steam in SI-Units. Springer-Verlag, Berlin. Selleck, F.T., Carmichael, L.T. and Sage, B.H., 1952. Phase behavior in the hydrogen sulfide-water system. Ind. Eng. Chem., 44: 9. Soave, G., 1972. Equilibrium constants from a modified Redlich-Kwong equation of state. Chem. Eng. Sci., 27: 1197-1203. Standing, M.B., 1974. Petroleum Engineering Data Book. Norwegian Institute of Technology, Department of Petroleum Engineering and Applied Geophysics. Takenouchi, S. and Kennedy, G., 1964. The binary system H,O-CO, at high temperatures and pressures. Am. J. Sci., 262: 1055-1074. Takenouchi, S. and Kennedy, G., 1965. The solubility of carbon dioxide in NaCl solutions at high temperatures and pressures. Am. J. Sci., 263: 445-454.
240
I. S$reide and C.H. whitson /Fluid Phase Equilibria 77 (1992) 217-240
Tsonopoulos, C. and Heidman, J.L., 1986. High pressure vapor-liquid equilibria with cubic equations of state. Fluid Phase Equilibria, 29: 391-414. Wiebe, R. and Gaddy, V.L., 1940. The solubility of carbon dioxide in water at various temperatures from 12 to 40°C and at pressures to 500 atmospheres. J. Am. Chem. Sot., 62: 815-817. Wiebe, R. and Gaddy, V.L., 1941. Vapor phase composition of carbon dioxide-water mixtures at various temperatures and at pressures to 700 atmospheres. J. Am. Chem. Sot., 63: 475-477. Wiebe, R., Gaddy, V.L. and Heins, C., 1933. The solubility of nitrogen in water at 50, 75, and 100°C at pressures to 700 atmospheres. J. Am. Chem. Sot., 55: 947-953. Yasunishi, A. and Yoshida, F., 1979. Solubility of carbon dioxide in aqueous electrolyte solutions. J. Chem. Eng. Data, 24: 11-14. Zemaitis, J.F., Clark, D.M., Rafal, M. and Scrivner, N.C., 1986. Handbook of Aqueous Electrolyte Thermodynamics, AIChE, New York.
217
Elsevier Science Publishers B.V., Amsterdam
Peng-Robinson predictions for hydrocarbons, CO,, N,, and H,S with pure water and NaCl brine Ingolf Sgreide a and Curtis H. Whitson Dept. of Petroleum. Eng., UNIT-NTH, 7036 Trondheim (Norway)
(Received March 4, 1991; accepted in final form February 2, 1992)
ABSTRACT Soreide, I. and Whitson, C.H., 1992. Peng-Robinson predictions for hydrocarbons, and H,S with pure water and NaCl brine. Fluid Phase Equilibria, 77: 217-240.
CO,, N,
Attempts at predicting mutual solubilities with a conventional cubic equation of state (EOS) including the effect of salts in the aqueous phase have so far been limited. The main purpose of this work is to provide a simple and novel approach for predicting mutual solubilities of brine/hydrocarbon mixtures with an EOS at high pressures and temperatures, including the effect of salinity in the aqueous phase. The Peng-Robinson EOS * has been applied in this study with two modifications: (1) an o-term in the EOS constant a has been developed specifically for the water/brine component as a function of sodium chloride (NaCl) brine salinity and pure water reduced temperature, T,, and (2) two sets of binary interaction parameters (BIP) in the classical mixing rule for mixture EOS constant a have been determined as a function of acentric factor, temperature, and salinity. Experimental data of vapor pressures and mutual solubilities provide the basis for the proposed methods. Applications of the methods described include phase behavior prediction of reservoir gas-oil/brine systems at high pressures, including (11 gas solubility in water/brine and (2) water solubility in hydrocarbon reservoir fluids.
INTRODUCTION
Most naturally occurring petroleum reservoir fluids contain water or brine. Conventional equations of state (EOSs), e.g. the PR EOS or the Correspondence
to: I. Soreide, Norsk Hydro a/s, P.O. Box 200, Stabekk, N-1321, Norway. a Current address: see Correspondence address. * Robinson and Peng, 1978.
0378-3812/92/$05.00
0 1992 Elsevier Science Publishers B.V. All rights reserved
218
I. S@reide and C.H. Waitson /Fluid Phase Equilibria 77 (1992) 217-240
Soave-Redlich-Kwong EOS (Soave, 19721, are not adequate for representing the special interaction of water molecules that determines phase behavior of the aqueous phase in hydrocarbon-water binary mixtures. Typically, the aqueous phase gas solubility may be predicted orders of magnitude in error, while predicted compositions of the hydrocarbon-rich phase(s) are reasonably accurate. Several modifications to cubic EOSs have been proposed to achieve a better representation of mixtures including pure water. Peng and Robinson (1980) propose two modifications of the original PR EOS to improve phase behavior prediction of hydrocarbon mixtures including water: first, a specific temperature dependency of the EOS constant a for water, c.u(T,>,is expressed &* = 1.008568 + 0.8215 (1 - ,“*),
T, < 0.72
(1)
Equation (1) results in improved water vapor pressure predictions in the range 0.44 < T, < 0.72 compared with the original PR EOS a-term. Secondly, two sets of binary interaction parameters (BIPs) are proposed for hydrocarbon/water binaries, one set for the non-aqueous phase(s) and one set for the aqueous phase. There is a clear empirical advantage of using this procedure, but it may lead to a thermodynamic inconsistency using two different values of constant a (Robinson et al., 1985). Despite this inconsistency, the approach should be valid away from critical conditions, which are usually not obtained for hydrocarbon/water mixtures. Peng and Robinson (1980) applied the modified PR EOS to several binary mixtures including water and hydrocarbons (C,-nC,) and nonhydrocarbons commonly found in petroleum mixtures (N,, CO,, H,S). A constant BIP for the non-aqueous phase(s) and a temperature-dependent BIP for the aqueous phase were found adequate to match experimental mutual solubility data with reasonable accuracy. A review of various EOS mixing rules for aqueous solutions is given by Michel et al. (1989). Effect
of salts in the aqueous phase
Attempts at predicting mutual solubilities with an EOS including the effect of salts in the aqueous phase have so far been limited. Most of the studies concerning this problem are performed at low pressures and temperatures, or use methods that are not readily applicable to systems containing supercritical gases. The work by Harvey and Prausnitz (1989) proposes an EOS for high pressure conditions using a rather complex EOS which accounts for intermolecular forces due to ionic effects, in addition to describing conventional intermolecular forces for non-electrolytes. In this model, two BIPS included in a cubic mixing rule are obtained from
I. Speide and C.H. Whitson /Fluid
Phase Equilibria 77 (1992) 217-240
219
room-temperature osmotic coefficients and Seconov (Setchenow) constants. Results show that the prediction is good for systems including pure water or brine with low salt content (< 1 molal). The salting-out effect is, however, underpredicted for systems with moderate to high salt content. The main purpose of this work is to provide a simple and novel approach for predicting mutual solubilities of brine/ hydrocarbon mixtures with a cubic EOS at high pressures and temperatures, including the effect of salinity in the aqueous phase. The PR EOS has been applied in this study with two modifications: (1) an a-term in the EOS constant a has been developed specifically for the water/ brine component as a function of NaCl brine salinity and pure water reduced temperature, and (2) two sets of BIPs in the classical mixing rule for mixture EOS constant a have been determined as a function of acentric factor, temperature and salinity. Experimental data on vapor pressures and mutual solubilities provide the basis for the proposed methods. Applications of the modified EOS include phase behavior prediction of reservoir gas-oil/ brine systems at high pressures, including (1) gas solubility in water/ brine and (2) water solubility in hydrocarbon reservoir fluids. HYDROCARBONSOLUBILITYIN WATER/NaCl BRINE SOLUTIONS Interstitial or connate formation water in a petroleum reservoir contains varying amounts of different salts, though mainly NaCl. The presence of salts in formation water reduces the gas solubility. A major part of this work is aimed at predicting the effect of brine salinity on gas solubilities in aqueous brine mixtures. Since data on some gas solubility of hydrocarbons in brine do not exist, “experimental” data were generated using measured gas solubilities in distilled water and Seconow salting-out coefficients to adjust for the salinity effect on solubility. This procedure is described below: A correction for gas solubility in a brine, S,, compared with gas solubility in distilled water, S,, is given by Seconow in terms of a salting-out coefficient, k,, and salinity (molal), c,: S”/S, = 10-k~C~~ (2) where S has units of moles/litre (molarity); k, coefficients have been presented in the literature for various hydrocarbon/ brine systems, as reviewed by Long and McDevit (1952) and Zemaitis et al. (1986). Cramer (1984) reports k, coefficients for a one molal methane/NaCl brine binary mixture in the temperature range 0-300°C (32-572°F). These data may be fitted using the following relation: k, = 0.1813 - 7.692 x 10-4T + 2.6614 x 10+T2 - 2.612 x 10-9T3 (3)
I. S@reideand C.H. Whitson/Fluid Phase Equilibria 77 (1992) 217-240
220
where T is in “F. Pawlikowski and Prausnitz (1983) suggest a linear relation for k, in terms of (Ei/k): k, =A, + B,( q/k)
(4)
where ci is the Lennard-Jones energy interaction parameter for the gas component and k is Boltmann’s constant, and A, and 8, are temperature-dependent constants given specifically for each salt at 25°C (77°F). If we assume an analogous k, temperature dependency for hydrocarbons other than methane, eqn. (4) can be used to obtain the shift in the salting-out coefficient for ethane, propane and n-butane, ksi, relative to that for methane, k,,. ksi = k,, + Aksi
i =
(5)
C,,C3, nC,
where Ak,i is expressed as
Aksi= ‘s[ (Ei/k) - (El/k)]
(6)
Pawlikowski and Prausnitz report B, = 3.56 x 1O-4 K m-l for NaCl brine. e/k may be related to the normal boiling point of the gas, Tbi.
(7)
Ei/k = 1.25T,, with Tbi in K. A general (3)-(7X
ksi correlation
results from combining
eqns.
k,, = 0.13163 + 4.45 x 10-4T,i
- 7.692 x 10-4T + 2.6614 x 10+T2 - 2.612 x 10-9T3
(8)
with T in “F and Tbl in K. Figure 1 shows a plot of salting-out coefficients versus temperature. The continuous lines represent k, values estimated from eqn. (8) and the symbols represent k, values for NaCl brines reported by Cramer (1984), Morrison (1952), Morrison and Billett (19521, Long and Chierici (1961) and Standing (1974). The accuracy of k, at high temperatures for C,, C, and nC, is questionable, but the importance of an accurate relation for these components at high temperatures is also small. Now that a general salting-out coefficient relation (eqn. (8)) has been developed, the hydrocarbon solubility in NaCl brine may be calculated to provide an “experimental” database of hydrocarbon solubility as a function of temperature and salinity as follows: (1) Obtain experimental data for hydrocarbon mole fraction in pure water, xi, at specified pressure and temperature conditions. (2) Calculate gas-water solubility, S, (S, = Nx,/(l -xi), where N is a constant dependent on units and brine properties).
I. Sereide and C.H. Whitson /Fluid
Phase Equilibria 77 (1992) 217-240
221
,, ,, o METHANE q 9 o ETHANE d A d PROPANE o o o n-BUTANE
ff”% 0 O,‘Oo5
10I,,,,
a 0
I,,@,,,,,,,,,,,,,,,,
REDU&
TE%t?AT&
30
35
T,
Fig. 1. Salting-out coefficients vs. hydrocarbon reduced temperature for hydrocarbon/NaCl brine mixtures: symbols represent reported coefficients from various sources, and solid lines represent eqn. (8).
(3) Calculate the ratio SJS,
from eqn. (21, with ksi estimated from eqn. solubility, S,, is then determined from the SJS, ratio
(8). Gas-brine and S,. (4) Finally, calculate S,/W + SJ.
the hydrocarbon
mole fraction in brine, xin (xi,, =
EOS MODIFICATIONS
Vapor pressure
Experimental vapor pressure data for water are given by Schmidt (1979) from 0 to 325°C [32 to 617”F], and for NaCl brine solutions of 0 to 5.0 molality from 80 to 325°C (176 to 617°F) by Haas (1976). The constant a of the PR EOS was modified for water/ brine to fit these data, resulting in a relation for the a-term as a function of pure water reduced temperature, T,, and salinity, c,,: (Y1’2= 1 + 0.4530[1 - T,(l - o.o103c:;‘)] + O.O034(T;_3- 1)
(9)
For water the PR EOS modified with eqn. (9) predicts vapor pressure within 0.2% error from 15 to 325°C [60 to 617”F]. NaCl brine vapor
I. Sereide and C. H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
222
pressures (176°F).
may be estimated
with about the same accuracy above 80°C
Aqueous and non-aqueous phase BIPs
The EOS modification proposed by Peng and Robinson (1980) using two sets of BIPs for water-hydrocarbon solutions has been adopted in this work. For a mixture including components i and j, two different EOS constants a are determined for the non-aqueous and the aqueous phase: a:* and aeQ, respectively. These are expressed as a function of the respective phase BIPs, kiyA and kz$Q, and mole fractions y and X. a!* = c lJ afiQ = i i
xyiyj(aia,)1’2(1
- k$*)
ixixj(aiaj)1’2(l
- kGQ)
w4
WV
j
Non-aqueous-in-aqueous phase solubilities
The sources for experimental hydrocarbon solubility data in pure water (C,-nC,/H,O) used in this work are listed in Table 1. Figure 2 shows that excellent agreement with measured methane solubilities in water can be obtained with the proposed EOS modifications (eqns. (9) and (10)) at various pressures and temperatures. The kzcQ values of eqn. (10) were determined by regression. The following correlation was developed: keQ=A fJ
0
+A 1T.+A rl
2 T? rl
(11)
where i = hydrocarbon components and j = water, and the constants A,, A, and A, are given in Table 2. The correlation may also be extrapolated to estimate kLcQ for pentane and heavier components. Figure 3 compares kcQ from eqn. (11) (solid line) with the regression-based kQQ (symbols).
TABLE 1 References
reporting hydrocarbon
gas solubilities in pure water
System
Reported by
p (bar)
T (“C)
Cl /I-W
CuIberson and McKetta (1951) Culberson and McKetta (1950) Kobayashi and Katz (1953) Reamer et al. (1952)
14-690 14-690 14-207 14-690
25-171 100-171 100-154 100-171
CZ /HP C3 /H,O n-C‘, /H,O
I. S@eide and C.H. Whitson /Fluid SYSTEM: 700 c
00001
Phase Equilibria 77 (1992) 217-240
223
C,/HpO 1
MOLE
‘
z
FRACTION
1 0.001
METHANE
IN
L
AQUEOUS
PHASE.
xc,
0.01
Fig. 2. Measured (symbols) and PR EOS calculated (solid lines) methane solubility in the aqueous phase at various pressures and temperatures.
Table 3 lists the physical properties used during development of eqns. (9) and (11). Figure 4 compares generated methane solubilities (using the above procedure) in a NaCl brine of various salinities at 104°C (220°F) (symbols) with methane solubilities calculated from the modified PR EOS using best-fit keQ values (solid lines). A ktQ correlation for hydrocarbon/NaCl brine binaries was developed from these data, and is expressed in terms of hydrocarbon Tri and c,: k;Q =A,(1
+ (Y,,c,,) +A&,(1
+ arc,,)
+A,T;(l
+ (Y~c,)
(12)
The constants of eqn. (12) are listed in Table 2. Equation (12) was developed for methane, ethane, propane and n-butane in 0 to 5 molal
TABLE 2 Constants in eqns. (11) and (12) A0 AI A2 a0
a1 a2
-
1.1120-1.73690-“~’ 1.1001+0.8360w~ 0.15742- l.O988o, 4.7863 x lo- 1304 1.4380 x lo-’ ’ 2.1547 x 1O-3
I. Sereide and C. H. whitson /Fluid Phase Equilibria 77 (1992) 217-240
224
0.1 ~""""',""""',""""',""""',
-0.3 r'JJ""J 05
l""""'l""'l""'l,"lt,'l' aEOD"CED
25
&ER*nJREf~,
Fig. 3. Aqueous phase interaction parameters for hydrocarbon/water binary systems as a function of hydrocarbon reduced temperature: symbols represent values determined by fitting experimental solubility data and solid lines are calculated using eqn. (11).
NaCl brine, for the pressure ranges given in Table 1, and at temperatures between 38 and 204°C (100 and 400°F). Figure 5 shows kc” versus temperature for methane dissolved in NaCl brine of varying salinity.
TABLE 3 Physical properties of components Component
Mol. weight
Carbon dioxide Hydrogen sulfide Nitrogen Methane Ethane Propane i-Butane n-Butane i-Pentane n-Pentane n-Hexane Water
44.0 34.1 28.0 16.0 30.1 44.1 58.1 58.1 72.2 72.2 86.2 18.0
304.2 373.2 126.1 190.6 305.4 369.8 408.1 425.2 460.4 469.6 507.4 647.3
PC (bar)
Acentric factor
73.8 89.4 34.0 46.0 48.8 42.5 36.5 38.0 33.8 33.7 30.1 221.2
0.2273 0.1081 0.0403 0.0108 0.0998 0.1517 0.1770 0.1931 0.2275 0.2486 0.3047 0.3434
194.7 212.8 77.3 111.6 184.6 231.1 261.3 272.7 301.0 309.2 341.9 373.2
I. S@reide and C.H. W&on SYSTEM:
/Fluid
Phase Equilibria 77 (I 992) 217-240
225
C,/NaCI-BRINE
BRINE SALINITY, c,. 00000000 m q ooao 0.66 m IA&&a 171 m ob0PP 3.42 m +++++513 m
MOLE
FRACTION
METHANE
IN AQUEOUS
PHASE,
xc!
Fig. 4. Generated (symbols) and PR EOS calculated (solid lines) methane solubility in the aqueous phase at 104°C as a function of pressure and brine salinity.
The following kGQ correlations were developed for binaries including water/brine and N,, CO, and H,S, based on experimental data referred to in Table 4:
0.2
7
BRINE 00000 OliDDD obc.*d bbbbb +++++
0.1
SYSTEM:
C,/NaCI-BRINE
(8 18 ‘I”,,
I”“““““,”
SALINIM.
c,.
0.0 0.65 1.71 2 56 3 42
.T Y ;
0.0
: v, ;
-0.1
5 -0.2
-0.3
30
Fig. 5. Aqueous phase interaction parameters for methane/NaCl brine binary systems as a function of temperature and brine salinity: symbols represent best-fit results and solid lines represent eqn. (12).
I. Sereide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
226
TABLE 4 References reporting nitrogen, water and NaCl brine
carbon dioxide and hydrogen sulfide solubilities
in pure
System
Reported by
p (bar)
T (“Cl
N, /H,O
Wiebe et al. (1933) O’Sullivan and Smith (1970) Wiebe and Gaddy (1940,194l) Prutton and Savage (1945) Takenouchi and Kennedy (1964) Yasunishi and Yoshida (1979) Selleck et al. (1952) Gillespie et al. (1984) Lee and Mather (1977)
14-103s lOO- 600 25- 510 25- 620 14- 970 1.0 20- 345 20- 220 lo60
25-100 52-125 12- 42 38- 50 150-350 15- 35 38-171 71-204 90-150
N, /brine Cb, /Ha0 CO2
/H,O
CO2 /brine CO2 /brine H,S/H,G H,S/H,G H,S/H,G
N,/NaCl
brine:
kcQ = - 1.70235( 1 + 0.25587~;!~) + 0.44338( 1 + O.O8126~,q;7~)T,, CO,/NaCl
brine:
kc0 = - 0.31092(1+
0.15587~~~~~~)+ 0.23580( 1 + 0.17837~,q;9~~)T,,
- 21.2566 exp( - 6.7222T,, - csW) H,S/NaCl
(13)
(14)
brine:
kcQ = - 0.20441+ 0.23426T,,
(15)
where i = N,, CO, or H,S, and j = water or brine. Figures 6 and 7 show keQ as a function of temperature and brine salinity for N,/ and CO,/NaCl brine binary mixtures, respectively. Symbols represent best-fit BIPs determined for the modified PR EOS, and solid lines represent BIPs calculated from correlation eqns. (13) and (14), respectively. The values increase linearly with increasing temperature for N,/NaCl brine mixtures. For COJNaCl brine mixtures it was observed that kcQ is a linear function of temperature above 150°C (300°F) and slightly non-linear below 150°C. Experimental data reporting solubility of CO, in NaCl brine for T < 150°C and at high pressures are not readily available. Therefore the dashed lines in Fig. 7 are not based on measured data, but rather a careful extrapolation of kij AQ determined at higher temperature. It is observed that the extrapolation of CO,/NaCl brine k,$” corresponds well to values obtained from solubility data reported by Yasunishi and Yoshida (1979) at atmospheric pressure (14.7 psia) in the range 15-35°C (60-95°F). A linear relation between kcQ and T,(H,S) was developed for the hydrogen sulfide/water binary mixture. This is illustrated in Fig. 8, which compares best-fit klqQ values obtained with the modified PR EOS and
I. Sereide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240 SYSTEM. 0.0
-
-02
-
i Q -0.3
-
J
N,/NaCI--BRINE
1
-01
227
I
2 In 3 -0.4
-
3 s Q -0.5
b
-0.6 t -o.7
r
0
I
1
25
1 I I
1
I
I
1
I
1
100 C
&PEW&E,
l
1 l
I
1
125
L I
1
Fig. 6. Aqueous phase interaction parameters for nitrogen/NaCl brine binary systems as a function of temperature and brine salinity: symbols represent best-fit results and solid lines represent eqn. (13).
SYSTEM:
CO/NaCI-BRINE
0.3
0.2
-0.2
~0000
Yasunishl and Yoshida 15 T p=, 0 bar
;::::
g: :g
c,=o-5
m
II,1,,IIIIII,,I,,I,,I,,I,IIIII,,,,,,,,,,,,,,
0
50
100 150 TEMPERATURE,
C
200
250
Fig. 7. Aqueous phase interaction parameters for carbon dioxide/NaCl brine binary systems as a function of temperature and brine salinity: symbols represent best-fit results and solid lines represent eqn. (14).
I. Stireide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
228
SYSTEM:
0.15
HzS/H,O
7
---___ gg----------___
0
:
PHASE
80
100 120 TEMPERATURE,
140
160
180
200
C
Fig. 8. Aqueous and non-aqueous phase(s) interaction parameters for hydrogen sulfide/water binary systems as a function of temperature: symbols represent best-fit results and solid lines represent eqns. (15) and (17) for k,qQ and k$*, respectively.
kcQ values from eqn. (15). Figure 9 compares experimental hydrogen sulfide gas solubilities with calculated values using the modified PR EOS and eqn. (15). The agreement is acceptable at low pressures. SYSTEM:
H&/Hz0
140v 20 _ _ _ 00 -
+
00000 30 oc 00000 71 oc 00000 104 oc +++++ 138 “C lxAfxl%b 171 oc
80 -
60 -
40 -
20 -
r,,,,,,~,,I~~~~~,~~~I~~~~~~~~~~~~~~~~~l~I
0900
MOLE
0.04
0.02
FRACTION
HIS
IN AQUEOUS
0.06
0.06
PHASE,
xw
Fig. 9. Measured (symbols) and PR EOS calculated (solid lines) hydrogen sulfide solubility in the aqueous phase at various pressures and temperature.
229
I. Sgreide and C.H. Whitson/Fluid Phase Equilibria 77 (I 992) 217-240 TABLE 5 Non-aqueous phase interaction light components
parameters,
ki,NA, for binary mixtures of water and various k?* I, 0.4850 0.4920 0.5525 0.5091 0.4778 0.1896 Eqn. 17
Component
Cl C, c3
n-C, N2 co2 H2S
Aqueous-in-non-aqueous phase solubilities
Experimental water solubility data in the non-aqueous phase for mixtures containing brine have not been available in the literature. Until such data become available it is recommended that the effect of salinity be modeled using the water/brine cy(c,)-term (eqn. (9)) in the PR EOS and a non-aqueous phase BIP value, k,y*, independent of salinity. k$* is basically independent of temperature, i.e. a constant kE* value results in water solubilities that are in good agreement with experimental data over the entire temperature range. kt” values are presented in Table 5. These are determined on the basis of pure water solubility data reported in references listed in Table 6. Figure 10 shows predicted water solubilities in the non-aqueous phase for a methane/NaCl brine mixture with varying brine salinity. The predicted reduction in water solubility for mixtures containing brine, relative
TABLE 6 References reporting non-hydrocarbon/water
non-aqueous systems
phase(s) water solubility for some hydrocarbon/
(bar)
System
Reported by
p
C,
/H,O
C,
/H,O
c3
/H20
Olds et al. (1942) Reamer et al. (1943) Kobayashi and Katz Reamer et al. (1952) Peng and Robinson (1985) Takenouchi and Kennedy (1964) Selleck et al. (1952) Gillespie et al. (1984) Lee and Mather (1977)
14-670 14-670 14-207 14-670 7-103 14-966 14-345 20-220 lo- 40
n-C, /H,O N, CO2
/H,O /H,O
H,S/H,G H,S/H,G H,S/H,G
T (“0 38-238 38-238 38-154 38-238 25-100 150-350 38-171 71-204 71
and
230
I. Sereide and C.H. whitson /Fluid Phase Equilibtia 77 (1992) 217-240 SYSTEM.
C,/NaCI-BRINE
600
T=lZl “C BRINE SALINITY, O? 0.0 q m 0 86 c+..%e 1.71 *u. 2.57 +u 3.42 *_cc!d 5.13
I
MOLE
0.01
FRACTION
2
WATER
5
IN C,-RICH
c,,
0.1
PHASE,
yv
2
Fig. 10. Measured (symbols) and PR EOS calculated (solid lines) water solubility in the non-aqueous phase of a methane/NaCl brine system at 121°C as a function of pressure and brine salinity.
to solubility for mixtures containing pure water, is for practical purposes independent of pressure and temperature. The ratio y,/yz calculated by the modified PR EOS is correlated against salinity in Fig. 11. The effect of
ODDOD OD(IDD a-
KATZ ET AL CALCULATED CALCULATED
BRINE
CORRECTION AT 38 ‘C AT 121 ‘C
SALINITY,
c,.
Fig. 11. Effect of brine salinity on water solubility in the non-aqueous vapor phase for a methane/NaCl brine mixture: “calculated” refers to use of the PR EOS modified with eqns. (9) and (10).
I. Sgreide and C. H. whitson /Fluid SYSTEM.
00000 00000 00000 +++++ *****
MOLE
38 71 93 138 171
FRACTION
Phase Equilibria 77 (1992) 217-240
231
H&/Hz0
o 0 “C “C “C
HpS
IN VAPOR
PHASE,
ytgi
Fig. 12. Measured (symbols) and PR EOS calculated hydrogen sulfide-rich vapor phase.
(solid lines) water solubility in the
salinity is clearly less than that reported by Dodson and Standing (1944) in the salinity range 0.0 to 0.6 molal, and is consistent with the correlation of Katz et al. (1959) up to a molality of about 3.0. The Katz y,/yz-relation can be expressed in terms of c, as y,(brine) yz(water)
p,(brine) 2: pz(water)
= 1 - 0 02865~‘.~ SW ’
(16)
where pw and y, represent vapor pressure and vapor phase mole fraction, respectively. For the H2S/H,0 system kt” is slightly dependent on temperature as shown in Fig. 8, resulting in the following relation: kF* ri = 0.19031-
0 .059653.l-l
i=H,S
(17)
Figure 12 shows that calculated water solubilities in the H,S-rich vapor phase compares well with experimental data, especially at pressures below 100 bar (1500 psi).
APPLICATIONS
In this section the proposed methods are applied to compare predicted mutual solubilities with measured data. Figure 13 compares predicted
I. S@reide and C.H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
232 SYSTEM: 700
,8
I
I
III,
I
I
C,/NaCI-BRINE, I,
I
I
,I
I
NaCI-BRINE c,=4.0
600
,I,
T=103 ”
’
“”
”
NaFl-j,ylJE ”
”
‘C ”
”
”
”
”
‘J
WATER
1
500 %
m
,-400
-
5 3300
-
E
a
$d;~LS
EXPERIMENTAL PR EOS PREDICTED
Fig. 13. Measured (symbols) and predicted (solid lines) methane solubility in the aqueous phase of a methane/NaCl brine system at 103°C as a function of pressure and brine salinity (experimental data from O’Sullivan and Smith, 1970).
methane solubilities in NaCl brine at 103°C with measured data reported by O’Sullivan and Smith (1970). Brine salinity ranges from 0.0 to 4.0 m, at pressures from 100 to 600 bar. It is observed that the PR EOS, modified with eqns. (9), (10) and (121, reproduces the experimental data accurately. Similar data are reported by Price et al. (1982) for C,/NaCl brine with salinity varying from 0.0 to 5.1 m, and pressures from 250 to 1550 bar. The comparison between predicted and measured data presented in Fig. 14 shows that C, solubility is slightly underestimated at 170°C at c, = 0.0, 1.9 and 5.1 m. The comparison shows that the deviations are most pronounced at high pressures (> 1000 bar). O’Sullivan and Smith also reported N, solubility in NaCl brine under similar conditions. A comparison of measured and predicted data is shown in Fig. 15. Again the modified PR EOS performs very well, except at C = 1.0 m where N, solubility is somewhat underpredicted. The aqueous phase liquid composition for a CO,/NaCl brine mixture is presented by Takenouchi and Kennedy (1965) at 150°C at pressures from 100 to 1400 bar. Figure 16 compares calculated and measured solubility data in the pressure range from 100 to 400 bar. Dodson and Standing (1944) reported measured solubilities of natural gas in pure water and in two oil-field brines. The pressure and temperature ranges in this study were 34.5-345 bar and 37.7-121°C. The salinity of the
I. Qreide and C. H. whitson /Fluid SYSTEM: 1750
C,/NaCI-BRINE,
Phase Equilibria 77 (1992) 217-240 T= 170
I,IIIIIII(IIIIIIIII,IIIJ~II~I,IIII,I NaCI-BRINE NO:‘-J;l;E c,=, 9 ”
233
‘C
WATER
1250 z m
1
- 1000 k! is 2
750
:
500
250
tL o?ooo I
MOLE
II
I
u c 10’)
0 005 FRACTION
1’8
METHANE
8
1’1 III )‘I 0 010 IN AQUEOUS
1’1 0015 PHASE,
1’8
l”j xc,
Fig. 14. Measured (symbols) and predicted (solid lines) methane solubility in the aqueous phase of a methane/NaCl brine system at 170°C as a function of pressure and brine salinity (experimental data from Price et al., 1982).
SYSTEM. 700
NoFl->:tE ” 600
N,/NaCI-BRINE,
T=103
“C
,IIIII,I~,II,,III,I(,,I,,,,,,,,,,,,,,,,,,,,,,,,,,NaCI-BRINE c,.=, 0
-
0
100
OPOOO MOLE
;YII;ILS
0.001 FRACTION
0 002 NITROGEN
WATER 0
EXPERIMENTAL PR EOS PREDICTED
0.003 ,,(,,,,,,,,,,, 0.004 IN AQUEOUS PHASE,
0.005 x,,,
Fig. 15. Measured (symbols) and predicted (solid lines) nitrogen solubility in the aqueous phase of a nitrogen/NaCl brine system at 103°C as a function of pressure and brine salinity (experimental data from &Sullivan and Smith, 1970).
I. Qreide and C. H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
234 SYSTEM.
CO,/NoCI-BRINE.
T= 150
OC
I~~~II~~“JI~~~I~‘JJIJJ~I”“~_
SYMBOLS,
tt
I
I
I
I
o”ooo MOLE
I
I
I
I
I
I
0.010 FRACTION
I
”
CO,
/
I
I
/
1 /
0 020 IN AQUEOUS
”
EXPERIMENTAL CALCULATED
11
1
0.030 PHASE,
”
1 ”
t
01
0.040 xco,
Fig. 16. Measured (symbols) and predicted (solid lines) carbon dioxide solubility in the aqueous phase of a carbon dioxide/NaCl brine system at 150°C as a function of pressure and brine salinity (experimental data from Takenouchi and Kennedy, 1964).
two brines denoted “Brine A” and “Brine B” were 8630 ppm (cSW= 0.15 m> and 34 1000 ppm (cSW= 0.60 m>, respectively. Although different types of salt were inchded in Brine A and Brine B, they were treated as NaC1
oPooo
,11111111111111111~IIIIII”‘~’
0 001 MOLE
FRACTION
0.003 0.002 NATURAL-GAS,
0 004 XNG
Fig. 17. Measured (symbols) and predicted (solid lines) natural gas solubility in the aqueous phase for the systems natural gas/water and natural gas/“Brine B” at 37.8”C (experimental data from Dodson and Standing, 1944).
I. Qreide and C.H. Whitson /Fluid
T=200 300
Phase Equilibria 77 (1992) 217-240
235
OF (93 3 “C)
-
MOLE
FRACTION
NATURAL-GAS,
X,,G
Fig. 18. Measured (symbols) and predicted (solid lines) natural gas solubility in the aqueous phase for the systems natural gas/water and natural gas/“Brine B” at 93.3”C (experimental data from Dodson and Standing, 1944).
brines. The natural gas used by Dodson and Standing contained 88.5 mol% C, and less than 1 mol% C,,; the average molecular weight of the gas was 19.
rY
2 -200
k! 2
Cl50
-
-
I? 100
-
50
0”000
I I I I I b I I, I I I I I I1 I I I1 I 0 003 0.002 0.001 MOLE FRACTION NATURAL-GAS, xw
I I I I 0 004
Fig. 19. Measured (symbols) and predicted (solid lines) natural gas solubility in the aqueous phase for the system natural gas/water at 121.1”C (experimental data from Dodson and Standing, 1944).
I. Sereide and C. H. Whitson /Fluid Phase Equilibria 77 (1992) 217-240
236 SYSTEM: c
NATURAL-GAS/WATER I
1 #‘II
4
$250 m
MOLE
FRACTION
WATER
IN VAPOR
PHASE,
yHa
Fig. 20. Measured (symbols) and PR EOS predicted (solid lines) water solubility in the hydrocarbon-rich vapor phase of a natural gas/water system at various temperatures (experimental data from Dodson and Standing, 1944).
To check performance of the proposed methods using the modified PR EOS for multicomponent mixtures, predicted natural gas solubilities were compared with the data of Dodson and Standing. These comparisons are presented in Figs. 17, 18, and 19 for 38, 94 and 121”C, respectively. It is shown that the predicted natural gas mole fraction in distilled water and in “Brine B” is very accurate, except for slight deviations at pressures above 250 bar at 121°C. Dodson and Standing also reported water solubility in the natural gas. Figure 20 shows that the prediction of these data is quite good when using the modified PR EOS and the kf;‘*‘s listed in Table 5. A k,y* value equal to 0.5 has been used for hydrocarbon/water binaries not listed in Table 5. For all hydrocarbon/ brine binaries eqn. (12) was applied to calculate ktQ.
CONCLUSIONS
Mutual solubilities have been accurately predicted with a modified,PR EOS for hydrocarbon/NaCl brine and some non-hydrocarbon/NaCl brine mixtures. The modifications consist of: (1) Using a modified a-term in the EOS constant a for the brine component as a function of water reduced temperature and brine salinity.
I. S@reide and C.H. Whitson /Fluid
Phase Equilibria 77 (1992) 217-240
231
(2) Using two sets of BIPs for each binary including water/ brine kbQ and kzyA for the aqueous phase and non-aqueous phase, respectively. k? is expressed as a function of NaCl brine salinity, hydrocarbon acentric factor and reduced temperature. Specific klyA correlations have also been developed for N,/, CO,/ and H,S/NaCl brine mixtures. For kt* a constant value is applied, except for klTA(H,S). The proposed methods have been demonstrated by comparing predicted and measured solubility of C,, N,, and CO, in NaCl brine of varying salinity. Acceptable accuracy has been obtained over a wide range of pressure and temperature conditions. Natural gas solubility in water and in two oil-field brines of varying salinity has been predicted with good agreement with measured data over a wide range of pressures and temperatures. Also, the predicted water solubility in natural gas agrees well with measured data.
ACKNOWLEDGMENT
This work was supported by the Nordic Council and Norwegian Foundation for Human and Technical Science.
LIST OF SYMBOLS
a, b a,,
al,
4 4, c SW C SW
k k% kk
ks MS P PC S” SW T Tb T,
4
a2,
a3
EOS constants constants of salting-out coefficient correlation constants of eqns. (11) and (12) constants of salting-out coefficient correlation brine salinity lo6 (m,/m, + m,) (ppm) brine salinity lo3 n,/m, (molality) Boltzmann’s constant aqueous phase interaction parameter for binary i, j non-aqueous phases interaction parameter for binary i, j salting-out coefficient, molality-‘, m-i molecular weight of salt (M, = 58.44 for NaCl) pressure (bar [psi]) critical pressure (bar [psi]) solution gas-brine ratio (mol-‘) (molarity) solution gas-water ratio (mall’) (molarity) temperature (“C [“F]) normal boiling point temperature (K [“RI) critical temperature (K [“RI)
238
I. Screide and C. H. whitson /Fluid Phase Equilibria 77 (1992) 217-240
T,
reduced temperature (T, = T/T,) normalized mole fraction of aqueous phase normalized mole fraction of non-aqueous phase
x, Yi
Greek letters a ai Aksi
E
w,
temperature-dependent parameter in EOS constant a constants of eqn. (12) shift in salting-out coefficient, m - ’ Lennard-Jones energy interaction parameter acentric factor
REFERENCES Cramer, SD., 1984. Solubility of methane in brines from 0 to 300°C. Ind. Eng. Chem. Process Des. Dev., 23: 300-305. Culberson, O.L. and McKetta, J.J. Jr., 1950. Phase Equilibria in Hydrocarbon-Water Systems. II The solubility of ethane in water at pressures to 10,000 psi, Trans. AIME, 189: l-6. Culberson, O.L. and McKetta, J.J., Jr., 1951. Phase equilibria in hydrocarbon-water systems. III The solubility of methane in water at pressures to 10,000 psi. Trans. AIME, 192: 319-322. Dodson, C.R. and Standing, M.B., 1944. Pressure-volume-temperature and solubility relations for natural gas-water mixtures. Drilling and Production Practice, API, 173-178. Gillespie, P.C., Owens, J.L. and Wilson, G.M., 1984. Sour water equilibria extended to high temperatures and with inerts present. Paper No. 34b presented at the AIChE Winter National Meeting, Atlanta, GA, March 11-14. Haas, J.L., Jr., 1976. Physical properties of the coexisting phases and thermochemical properties of the H,O component in boiling NaCl solutions. Geol. Surv. Bull., 1421-A and 1421-B. Harvey, A.H. and Prausnitz, J.M., 1989. Thermodynamics of high-pressure aqueous systems containing gases and salts. AIChE J., 35: 635-644. Katz, D.L., Cornell, D. and Vary, J.A., 1959. Handbook of Natural Gas Engineering. McGraw-Hill, New York. Kobayashi, R. and Katz, D.L., 1948. Methane-n-butane-water system in two- and three phase regions. Ind. Eng. Chem., 40: 5. Kobayashi, R. and Katz, D.L., 1953. Vapor-liquid equilibria for binary hydrocarbon-water systems. Ind. Eng. Chem., 45: 440-451. Lee, J.I. and Mather, A.E., 1977. Solubility of hydrogen sulfide in water. Ber. Bunsenges Phys. Chem., 81: 1021-1023. Long, F.A. and McDevit, W.F., 1952. Activity coefficients of nonelectrolyte solutes in aqueous salt solutions. Chem. Rev., 51: 119-169. Long, G. and Chierici, G., 1961. Salt content changes compressibility of reservoir brines. The Pet. Eng., B-25 to B-31. Ludecke, D. and Prausnitz, J.M., 1985. Phase equilibria for strongly nonideal mixtures form an equation of state with density-dependent mixing rules. Fluid Phase Equilibria, 22: 1-19.
I. S)reide and C.H. Whitson /Fluid
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